In the MCU, Jotunhiem isn't somewhere that's fully explained, so we, as fans, come up with our own headcanons. Here's a few of my own for Jotunheim and their culture, along with what I think happened when Odin found Loki.
- Culture
In the mythology, they are depicted as being very wild and chaotic. While I enjoy the idea, I like giving wild things the benefit of the doubt, and give them some kind of culture. With Jotuns, I think a big part of their culture is the markings they have on them. There's a difference between the markings of royalty and of a soldier. While some are inherited at birth (royalty, other social classes), they can also be earned (being a soldier, much like how the military gives out rewards).
Their markings are very meaningful to them and it's something that they accept as their culture. They also hold the Casket of Ancient Winters at a high standard, as it's their power source and therefore a huge part of their own culture. They would keep it someplace safe, somewhere where it would be unharmed. That place would likely be a temple. Similar to our churches or synagogues, they keep their most valuable objects in the temple, where they can have that bit of "worshipping".
I believe they would also pride themselves on hunting and craftsmanship, the males often going out on hunting trips and others trying to make clothing that would be suitable for them.
For the females, they are a large part of the cultures as well. While I believe it would have been forgotten in many years of culture, the Jotuns have the idea that the female Jotunar are much more important than the men, as the women quite literally ensure that their species survives. The men do most of the hunting (however there have been women who have hunted), and women have the children and raise them. Since the women are seen as important to the culture, I think they would also hide the women away in times of battle, war or just threats in general. This would be why we don't see any female Jotunar in the Thor movie.
As women are seen as important to their kind, I believe marriage would be a big deal within their culture.
- Belief System
To me, the Jotunar definitely come in different shapes and sizes. Gerdr in Norse Mythology is a GREAT example of this. But MCU Jotunar are slightly different. In my mind, the idea that the MCU Jotunar come in different shapes and sizes is still true, but it's believed that the smaller Jotunar are capable of using seidr, or having magic similar to Loki's shapeshifting and illusions. As said previously in my Status Classes post, the Jotunar wouldn't care much for the status of class unless it was royalty. I can see their culture with royalty being similar to that of the Egyptians, just with less... interbreeding between families. I'm sure a Jotun healer saw the deformities and was like "Something isn't right.." and they mostly tried to fix that tradition, with some still following it.
Marriage, as stated above, would have been a big deal. Laufey doesn't seem to have any other family, so his marriage to Fárbauti would have also been a big deal (yes, Fárbauti is Loki's father in Norse Mythology and Laufey is his mother, but according to the MCU, they're swapped).
So when Fárbauti gave birth to a small Jotun, while in Aesir culture it would be considered a 'runt', I don't think that the Jotun would have thought of him as such.
- What really happened
In some concept art for the Loki series, we can see Fárbauti, Loki's mother, leaving him.
In Thor, Odin says that when he went into the temple, he found a baby. We know that that was Loki, and something that I was really thinking about was: Why leave a runt in a temple, where you keep the most sacred things? I don't think they abandoned Loki, but they were merely keeping him in a safe place until the battles were over. Unless the Jotunar wanted to place the Casket of Ancient Winters were they thought it was unsafe (which they wouldn't because it's their power source), putting something in the temple would be a way to protect what they thought was important. So after Odin took their power source, I think he just strolled in, took the baby and left.
These are all just my headcanons! I like to think that this is really what happened, but of course, we will never know because history is told by the victors and the victor was a 'great' dad./sar